3 A Genetic Model for AM in Plant Breeding Populations: Association as Conditional ProbabilitiesMarkerPopulation genetics theory(Hedrick 2005)Recombination (c)Breeding PoolGene={a}Marker={m,M}Selection on A or M (w)Recombination (c)New Parent (A,M)t generationsPr(A,M)=φPr(a,M)=θPr(a,m)=1-φ-θPr(A,m)=0Pr(A|M,c,t,φ,θ,w)“Probability of a plant with marker allele M to have gene allele A, t generations after the introduction of A”

4 Recombination x initial frequency of M in the breeding poolFreq. new parent: φ=0.05Relative fitness: w=1Freq. M in original population = θFreq. Recombination c~8~18θ=0θ=0.05θ=0.25θ=0Pr(A|M)A novel marker allele at 10 cM distance can be more predictive of the QTL allele than an allele 1 cM away if it was present in the original pop at a freq of 0.05t Generations

5 Recombination x selection for MFreq. new parent: φ=0.05Relative fitness: w = 4 (red), 2 (green), 1.25 (blue)Freq. M in original pop: 0Freq. Recombination: c = 0.01, 0.05, 0.10The generation at which the marker is depleted [Pr(A|M)=Pr(A)], depends on the selection intensity applied;The final frequency of A depends on selection and tightness of linkage between marker and gene.Pr(A|M)Pr(A)Generations

6 SummaryIn plant breeding populations, the locus most associated with the trait is not necessarily the closest locus;Loosely linked markers can still be useful for MAS if high intensity of selection is applied.

7 MAS for Complex Traits: IssuesAccurate detection and estimation of QTL effectsPre-existing marker alleles in a breeding population can be linked to non-target QTL allelesMultiple QTL alleles can have different relative valuesGene x gene and gene by environment interactions

9 Association Mapping versus QTL MappingAssociation Mapping can be conducted directly on the breeding material, therefore:Direct inference from data analysis to breeding is possiblePhenotypic variation is observed for most traits of interestMarker polymorphism is higher than in biparental populationsRoutine variety trial evaluations provide phenotypic dataAssociation Mapping provides other useful information about:Organization of genetic variation in relevant breeding populationsNovel alleles can be identified and their relative value can be assessed as often as necessary

10 Association Mapping versus QTL MappingType I error (false positives) can be higher because of:Unaccounted population structureSimultaneous selection of combinations of alleles at different lociHigh sampling variance of rare allelesType II error can be higher (low power) because of:Lower LD than in biparental mapping populationsUnbalanced design due to differences in allele frequenciesA larger multiple-testing problem because of lower LD

12 Types of Populations Germplasm Bank Collection Synthetic PopulationsA collection of genetic resources including landraces, exotic material and wild relatives.Synthetic PopulationsOutcrossing populations (either male-sterile or manually crossed) synthesized from inbred lines. May be used for recurrent selection.Elite LinesInbred lines (and checks) manipulated with the objective of releasing new varieties in the short term.

22 Definition of a baseline-LD specific for our sampleDefined as the 95th percentile of the distribution of r2 among unlinked locir2 estimates above this value are probably due to genetic linkageBaseline LD for this sample: r2 =Normal curveNormal Distr. 95th percentileLD baselineLD baseline

30 Conclusions Linkage DisequilibriumVariation in LD across the genome can be characterized in relevant germplasmMarkers closely linked to QTL of interest can be identified and allelic effects quantifiedAssociation Mapping as a Breeding StrategyFor recurrent selection, markers could be used to carry information from a “good year” to a “bad year”In pedigree breeding, markers could carry information about traits of interest from replicated field trials to single row or single plant selectionAllelic values of previously identified alleles can be updated annually based on advanced trial data combined with genotypic dataNew alleles can be identified and characterized to determine their relative valueA selection index can be used to incorporate both phenotypic and molecular data

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